Question

Решите уравнения. 1) x2 - 4 = 0; 2) 9x2 = 0; 3) 5x2 = 0; 4) - 14x2 - 56 = 0; 5) x2 - 33 = 0; 6) 14x2 = - 140x; 7) -x2 - 8x = 0; 8) 2х2-4х=х(4х-3)

Answer 1

1. Х²=4

Х1=2

Х2=-2

2. Х=0

3.х=0

4. -14х²=56

Х²=-4

Корней нет

5.х²=33

Х1= корень из 33

Х2= -корень из 33

6. 14х²+140х=0

14х(х+10)=0

Х=0 и х=-10

7. -х(х+8)=0

Х=0 и х=-8

8. 2х²-4х=4х²-3х

2х²-4х²-4х+3х=0

-2х²-х=0

-х(2х+1)=0

Х=0 и 2х=-1

Х=0 и х=-0,5

Answer 2

Ответ:

Объяснение:

1) x² - 4 = 0;  х²=4; х=±√4; х=±2;  х1=-2; х2=2

2) 9x² = 0;  х=0

3) 5x² = 0;  х=0

4) - 14x² - 56 = 0;

-14(х²+4)=0; -14≠0;х²+4≠0

ответ: Уравнение не имеет действительных корней

5) x² - 33 = 0;  x²=33; х=±√33; х1=-√33; х2=√33

6) 14x² = - 140x;

14x²+140х=0

   14х(х+10)=0

х1=0; х2=-10

7) -x² - 8x = 0;

  -х(х+8)=0

х1=0 либо х2=-8

8) 2х²-4х=х(4х-3)

2х²-4х=4х²-3х

2х²-4х-4х²+3х=0

-2х²-х=0

-х(2х+1)=0

х1=0; х2=-1/2=-0,5

Answer 3

1. x^2 - 4 = 0: To solve this equation, we can factor the left side:

(x - 2)(x + 2) = 0

Setting each factor equal to zero gives us:

x - 2 = 0 or x + 2 = 0

Solving these equations gives us two solutions:

x = 2 or x = -2

2. 9x^2 = 0: Dividing both sides of the equation by 9 gives us:

x^2 = 0

Taking the square root of both sides, we get:

x = 0

So the only solution is x = 0.

3. 5x^2 = 0: Dividing both sides of the equation by 5 gives us:

x^2 = 0

Taking the square root of both sides, we get:

x = 0

So the only solution is x = 0.

4. -14x^2 - 56 = 0: First, let's divide the entire equation by -14 to simplify it:

x^2 + 4 = 0

Subtracting 4 from both sides, we have:

x^2 = -4

Since the square of a real number cannot be negative, this equation has no real solutions.

5. x^2 - 33 = 0: Adding 33 to both sides of the equation, we get:

x^2 = 33

Taking the square root of both sides, we have:

x = ±√33

So the solutions are x = √33 and x = -√33.

6. 14x^2 = -140x: First, let's divide the entire equation by 14x to simplify it:

x = -10

So the solution is x = -10.

7. -x^2 - 8x = 0: Factoring out an x from the equation, we get:

x(-x - 8) = 0

Setting each factor equal to zero gives us:

x = 0 or -x - 8 = 0

Solving the second equation for x, we have:

-x = 8

Multiplying both sides by -1, we get:

x = -8

So the solutions are x = 0 and x = -8.

8. 2x^2 - 4x = x(4x - 3): Expanding the right side of the equation, we have:

2x^2 - 4x = 4x^2 - 3x

Rearranging the equation, we get:

4x^2 - 3x - 2x^2 + 4x = 0

Combining like terms, we have:

2x^2 + x = 0

Factoring out an x, we get:

x(2x + 1) = 0

Setting each factor equal to zero gives us:

x = 0 or 2x + 1 = 0

Solving the second equation for x, we have:

2x = -1

Dividing both sides by 2, we get:

x = -1/2

So the solutions are x = 0 and x = -1/2.